Computer analysis of Cs3Sb photocathodes

Solid-State Electronics Vol. 32, No. 3, pp. 243-246, 1989 Printed in Great Britain. All rights reserved

0038-1101/89 $3.00+0.00 Copyright © 1989 Pergamon Press pie

COMPUTER ANALYSIS OF Cs3Sb PHOTOCATHODES B. YANG Xian Institute of Optics & Precision Mechanics, Academia Sinica, Xian, Shanxi, Peoples Republic of China

(Received 5 July 1988; in revisedform 19 September 1988) Abstract--The transport of photoelectrons through Cs3Sb photocathodes is studied by the Monte Carlo simulation technique. The mean free path, for energy loss to phonons, of energetic electrons in Cs3Sb has been found to be about 25 A. The modulation transfer function (MTF) of the Cs3Sb photocathodes, energy distribution and transit time spread (TTS) of emitted electrons have been obtained. In particular, the energy distribution of the emitted electrons has a very good agreement with the measured results. Computed results indicate that both the energy spread, defined as the full width of half-maximum of the energy distribution and the TTS of emitted electrons are significantly influenced by the incident photon energy. It is also proposed that reducing the thickness of the Cs3Sb photocathode is an effective method of decreasing the energy spread and TTS of emitted electrons.

1. I N T R O D U C T I O N The Cs3Sb photocathode has been used widely and studied extensively since its invention in 1936[1-3], but is still little understood. This situation has interfered with its application in some special cases. In this paper, computer analysis of Cs3Sb photocathodes based on Monte Carlo simulation is described. The principle of the method is to model the electron trajectory in a Cs3Sb layer from photoexcitation to emission. As the photoemission process is too complicated for us to completely simulate for a real situation, we use three general assumptions in our calculation. (1) The energy of the photoexcitation electron is equal to incident photon energy. (2) In Cs3Sb, other energy loss process are negligible relative to the energy loss by phonon scattering, i.e. by interaction with the lattice. (3) Photoexcitation and emission times are negligible compared to that of energy relaxation and transport to the surface.

2. SIMULATIONMODEL Since Cs3Sb is a P-type semiconductor for which the acceptor level lies 0.5 eV above the top of the valence band, or 1.55 eV below the vacuum level as shown in Fig. 1, it can be concluded that most of the electrons are emitted originally from the acceptor level when a helium-neon laser serves as the light source. The simulation procedure can be described by the well-known three-step process: (1) photoexcitation of electrons into the conduction band; (2) energy relaxation and transport to the surface; (3) emission into vacuum. We explain it in detail as follows. (1) When the photon energy hv is such that hv >I Eg-Ed, transitions occur between the acceptor

level and the conduction band. Supposing the Z-axis is normal to the Cs3Sb layer, then the light intensity absorbed in Cs3Sb has an exponential distribution of the form[4].

g(z) = (1 - R)Aot exp(--ctz),

(1)

where R is the optical reflexion coefficient, A is the incident light flux in photons, ct is the absorption constant of the Cs3Sb. Choosing X, Y and Z as the axes of the cortesian coordinates, the position of an electron is described by the random numbers. For conveniences in the calculation the cathode diameter is set equal to one. X = 2RI - 1

(2)

Y = 2Rz - 1

(3)

If X 2 + yz >/1, two new random numbers R 1 and R 2 are selected and new values of X and Y computed (R) and R2 denote random variables independently and uniformly distributed in the interval (0,1). The probability of a particular Z coordinate is described by the density g(z) [eqn (1)]. The energy of the electron is assumed to be equal to the photon energy. (2) The photoelectron created by the photon within the solid is a hot electron, i.e. its energy is above that of the other electrons in the solid as determined by the thermal equilibrium. The probability of this hot electron reaching the vacuum interface depends on the energy loss processes to which it is exposed on its path. The free path length of an electron (i.e. the length of the path from one collision to another) is a random variable, it can be taken as any positive value with the probability.

,., where 2 is the mean free path. 243

244

B. YANG cathode for various kinds of radiation. Similar distributions are obtained, and the corresponding energy spreads for different wavelengths are 0.11 eV at 6328 ~, 0.20 eV at 5245 A and 0.30eV at 4579 A. Figure 2 also shows the energy distribution curve which was measured by Chungsin[6]. The calculated and measured result have a very good agreement at 6328/~ wavelength. The simulation results shown in Fig. 2 are obtained by using the following input data: the electron mean free path 2 = 2 5 A , and the phonon speed u = 7 x 103 m/s.

Vo¢ugm 1 Conduction bond

0

(t.6 eV)

J

Eo (0.45 eV)

A_ Ed (0.5 eV)

VoLence bond

T

Fig. 1. Energy diagram of caesium antimonide,

After an electron collides with a phonon, the probability density of the electron diffusing within the angle 0 - - 0 + dO and ~o--~0 + d~0 is

P(O) = sin 0/2

0 < 0 ~
(5)

P(q~) = 1/2x

0 < q~~<2n

(6)

where 0 and q~ are the polar and azimuthal angles respectively. The energy loss per collision, fiE, when an electron is scattered through an angle fl is given approximately by[5]:

6E = 2mvu sin(/3/2),

(7)

where v is the velocity of the electron, m is the mass of the electron and u is the phonon speed. (3) When the electron reaches the surface, its energy can be expressed in the form: E

=

0.5m (v 2, + v~ + v2~).

(8)

The escape probability of an electron on the surface is:

P(E) =

{1.00 mv~/2 >~E a mv2z/2 < Ea

(2) TTS o f emitted electrons The TTS of emitted electrons is very difficult to measure but is important in the application of Cs3Sb photocathodes. Figure 3 shows the TTS of emitted electrons from a Cs3Sb photocathode for various kinds of radiation. Similar pulse height distributions are obtained, and the corresponding FWHM for different wavelengths are 30 fs at 6328 A, 70 fs at 5245 A and 1I0 fs at 4579 ~.

(3) M T F of Cs3Sb photocathodes The MTF of Cs3Sb photocathodes with various thicknesses which are illuminated by 6328/~ radiation are shown in Fig. 4. The MTF of C%Sb photocathodes of 300 ~, thickness which are illuminated by radiation of various wavelengths are also obtained, as shown in Fig. 5. In this calculations, we assume the incident light to be a delta pulse. Thus the MTF are calculated strictly according to the definition.

200

(9)

" ~

where E a is the electron affinity. In each step of the multiplication process, first of all the energy and position of each electron is calculated from eqns (1), (2) and (3). The free path, scattering angle and energy loss are then obtained from random numbers based on eqns (4)-(7) respectively. In the next step, it is determined whether the electron has a collision with another phonon or emits into the vacuum. The electron is followed from collision to collision until it emits into the vacuum or until its energy is less than vacuum level. If the electron emits into the vacuum, its history is terminated, and the coordinates of a new electron are generated. In the simulation process, 4000 trajectories are traced to obtain the final results.

..... I

hu = 1.946 eV hi, = 2.416 eV hi, • 2.71,5 eV

150

"6 .Q

100 E

Ff L,

"D 0

50

1 I I 300

,I 600

I I

I 900

I 1200

ELectron energy (rneV)

3. SIMULATIONRESULTS

(1) Emitted energy distribution Figure 2 shows the calculated spectrum of photoelectrons emitted from a caesium antimonide photo-

Fig. 2. The energy distributions of emitted electrons. The pulse height distributions are simulated results for different photon energies. The curve is the measured result for 6328 A photon radiation. The thicknesses of the photocathodes are all 300 ~,.

Computer analysis of Cs3Sb photocathodes

245

200 !--i I I !-1so "

I

L

.....

hv • 2 . 7 t 5

l -- .n

I

I

hv

1.0

hl, • 1 . 9 4 6 eV flu.2.416 .V

• 1 . 9 4 6 eV

eV

i b. I--

'~

( !

"~ 100

t_

--J

i ~~-!_.

~

1-.

~............

0.9

I

I ZOO

10o

I 300

I 400

I 500

f (tp/mm)

I I

I 50

0

I 100

Fig. 5. MTF of a caesium antimonide photocathode for various incident photon energies. The thickness of the photocathode is 300 ,~.

--~ 150

Time (fs)

Fig. 3. The simulated TTS of emitted electrons for different photon energies. The thicknesses of the photocathodes are all 300 A.

4. DISCUSSION

As shown in Figs 2, 3 and 5, the incident photon energy has a great influence on the M T F of a Cs3Sb photocathode, and on the energy spread and TTS of the emitted electrons. As the photon energy increases, photoelectrons from deeper regions can reach the surface with an energy above vacuum level. This results in an increased spread and TTS of the emitted electrons and a reduced MTF of the photocathode. As the thickness increases above 300/~, there is little further influence on the M T F of the photocathode, or the TTS and energy spread of the emitted electrons. The reason for this is that the escape depth of the electrons is about 250 A,. Therefore only those electrons that are created within this region have a possibility of contributing to the emission current. To be a good photocathode, the energy spread and TTS of the emitted electrons should be as small as

possible. Through calculation, we find that both of them can be reduced by decreasing the thickness of the Cs3Sb photocathode below the electron escape depth. But we will be faced with a trade-off between these characteristics and that of photo-sensitivity. The MTF ofa Cs3Sb photocathode, and the TTS and energy spread of the emitted electrons are shown in Figs 4, 6 and 7 for a thickness of 150/~. Comparing with the distributions for thicker films, we find all of them have been improved. $. CONCLUSION

We have calculated the MTF of Cs3Sb photocathodes, and the TTS and energy spread of emitted electrons. We have shown that the incident photon energy has a significant influence on their magnitudes. This follows from the fact that diffusion numbers increase with increasing photon energy whenever that energy is greater than the vacuum level. However when the cathode thickness is greater than 300.~, changes in thickness have no great influence on the performance of the Cs3Sb photocathode.

250 d • 150 A

1.00

200

"6 .~

150

E_ LA. I-:E

¢

I00

',~ o.

~: 5o I 100

0.99

o

I 1oo

I zoo

i 300

i 400

i 500

f (Lp/mm)

Fig. 4. MTF of a caesium antimonide photocathode for various thicknesses. It is illuminated by 6328 A, light. S.S.E. 32/T--E

I 200

I 3oo

I 40o

ELectron e n e r g y ( m e V )

Fig. 6. The simulated energy distribution of emitted electrons, from a caesium antimonide photocathode with 150 ,~ thickness. It is illuminated by 6328 A light.

246

B. YANG thickness of the Cs3Sb photocathode. As shown in Figs 6 and 7, the energy spread and TTS of emitted electrons are reduced to about 0.45eV and 10fs respectively when the thickness is reduced to 150/~.

25O

200

150

Acknowledgements--I am thankful to Professor H. Xun, Professor N. Hanben and Dr S. Y. Long for their helpful discussions and encouragement. I also wish to thank Dr Paul Key for his revision of the paper.

~= t 0 0

>* o

50 " - 1 50

60

90

120

Time (fs)

Fig. 7. The simulated "ITS of emitted electrons from a caesium antimonide photocathode with 150/~ thickness. It is illuminated by 6328/~ light.

Finally, we point out that the M T F of Cs3Sb photocathodes, and the TTS and energy spread of emitted electrons can be reduced by reducing the

REFERENCES

1. A. H. Sommer, Photoemissive Materials. Wiley, New York (1968). 2. W. E. Spicer, Phys. Rev. 125, 1297 (1962). 3. W. E. Spicer and C. N. Rerglund, Rev. scient. Instrum. 35, 1665 (1964). 4. A. A. Turnbull and G. B. Evans, J. appl. Phys. 7, 15 (1968). 5. R. A. Simith, Semiconductors. Cambridge University Press, Cambridge (1978). 6. Chungsin Lee, J. appl. Phys. 54, 4597 (1983).